Andreas Cap (Universität Wien): Quaternionic complexes

Abstract: Almost quaternionic and quaternionic structures are interesting from at least two points of view. On the one hand, any quaternion-Kaehler manifold automatically carries a quaternionic strucutre. On the other hand, almost quaternionic geomtry is a natural higher dimensional analog of conformal goemetry in dimension four, with quaternionic structures playing the role of self-dual conformal structures. In my talk I will survey joint work with V. Soucek on differential operators which are intrinsic to such structures. For quaterninic structures, we obtain a large family of natural complexes, many of which can be proved to be elliptic. In particular, we construct an elliptic deformation complex in the category of quaternionic structures.